We verify a conjecture of Vershik by showing that Hall's universal countable locally finite group can be embedded as dense subgroup in the isometry Urysohn space and automorphism random graph. In fact, we show same for all groups known infinite ultraextensive spaces. These include, addition, rational space, ultrametric spaces, Kn-free graph n≥3. Furthermore, actions on metric spaces or some rel...

In this paper, we deal with Molaei’s generalized groups. We definethe notion of a fuzzy generalized subgroup with respect to a t-norm (orT-fuzzy generalized subgroup) and give some related properties. Especially,we state and prove the Representation Theorem for these fuzzy generalizedsubgroups. Next, using the concept of continuity of t-norms we obtain a correspondencebetween TF(G), the set of ...

The evolution of standard model gauge couplings is studied in a nonsupersymmetric scenario in which the hierarchy problem is resolved by Higgs compositeness above the weak scale. It is argued that massiveness of the top quark combined with precision tests of the bottom quark imply that the right-handed top must also be composite. If, further, the standard model gauge symmetry is embedded into a...

In this paper we study the generic, i.e., typical, behavior of finitely generated subgroups of hyperbolic groups and also the generic behavior of the word problem for amenable groups. We show that a random set of elements of a nonelementary word hyperbolic group is very likely to be a set of free generators for a nicely embedded free subgroup. We also exhibit some finitely presented amenable gr...

In this paper, new examples of weakly symmetric spaces in the sense of A. Selberg 14] are constructed. Let G be a connected, simply-connected, simple Lie group of hermitian type and K a maximal compactly embedded subgroup of G such that D = G=K is an irreducible classical bounded symmetric domain. Let G 1 and D 1 be circle extensions of G and D, respectively. The factor of automorphy induces a ...

Let $G$ be a group and $Aut(G)$ be the group of automorphisms of‎ ‎$G$‎. ‎For any natural‎ number $m$‎, ‎the $m^{th}$-autocommutator subgroup of $G$ is defined‎ ‎as‎: ‎$$K_{m} (G)=langle[g,alpha_{1},ldots,alpha_{m}] |gin G‎,‎alpha_{1},ldots,alpha_{m}in Aut(G)rangle.$$‎ ‎In this paper‎, ‎we obtain the $m^{th}$-autocommutator subgroup of‎ ‎all finite abelian groups‎.

BACKGROUND Oncocytic carcinomas (Hürthle cell carcinomas [HCCs]) are commonly considered a subgroup of follicular thyroid carcinomas (FTCs). Recent characterization of a subgroup of "Hürthle cell" papillary thyroid carcinomas (PTCs) was based on the identification of PTC-specific RET hybrid oncogenes in HCCs. METHODS We examined 27 HCCs, 4 oxyphilic FTCs, 5 oxyphilic PTCs, 2 poorly differenti...

In this paper we obtain a curvature estimate for embedded minimal surfaces in a three-dimensional manifold of positive Ricci curvature in terms of the geometry of the ambient manifold and the genus of the minimal surface. It should be mentioned that there are two main points in our result: One is the absence of a stability assumption and the other is the requirement of being embedded. Most know...

We devise a ternary operation for combining three quantum states: it consists of permuting the input systems in a continuous fashion and then discarding all but one of them. This generalizes a binary operation recently studied by Audenaert et al. [ADO16] in the context of entropy power inequalities. Our ternary operation continuously interpolates between all such nested binary operations. Our c...